A can finish a piece of work in 15 days and B can do it in 10 days. They worked together for 2 days and then B goes away. In how many days will A finish the remaining work?

A's 1 day work = $\dfrac{1}{15}$

B's 1 day work = $\dfrac{1}{10}$

(A + B)'s 1 day work = $\dfrac{1}{15} + \dfrac{1}{10}$

= $\dfrac{2 + 3}{30}$

= $\dfrac{5}{30}$

= $\dfrac{1}{6}$

(A + B)'s 2 day work = $\dfrac{1}{6} \times 2$

= $\dfrac{1}{3}$

Remaining work = $1 - \dfrac{1}{3}$

= $\dfrac{3}{3} - \dfrac{1}{3}$

= $\dfrac{2}{3}$

No. of days taken by A to finish the remaining work = $\dfrac{\text{Remaining work}}{\text{B's 1 day work}} = \dfrac{\dfrac{2}{3}}{\dfrac{1}{15}}$

= $\dfrac{2 \times 15}{3 \times 1}$

= $\dfrac{30}{3}$

= $10$

Hence, A will take 10 days to finish the remaining work.